Randomized Algorithms
CS648
Lecture 21
Random Walk and Electric Networks
1
OVERVIEW AND MOTIVATION
2
What do we know about Random walk till now?
We have discussed uniform random walk on
A line.
A complete graph.
Two complete graphs joined by an edge (M

Randomized Algorithms
CS648
Lecture 14
Expected duration of a randomized experiment
Part II
1
REVISITING
SOME DISCRETE MATHEMATICS
2
Recurrence 1
For any ,
Question: What is the smallest value of such that for a given ?
Answer: ?
For any ,
for some
Ques

Randomized Algorithms
CS648
Lecture 15
Randomized Incremental Construction
(building the background)
1
Partition Theorem
A set of events , defined over a probability space (,P) is said to induce a
partition of if
=
=
for all
B
Partition Theorem:
P(B) =

Randomized Algorithms
CS648
Lecture 9
Random Sampling
part-I
(Approximating a parameter)
1
Overview of the Lecture
Randomization Framework for estimation of a parameter
1. Number of balls from a bag
2. Size of transitive closure of a directed graph
. An I

Randomized Algorithms
CS648
Lecture 12
Hashing - II
1
RECAP OF LAST LECTURE
Problem Definition
called universe
and
Examples:
,
Aim
Given a set , build a data structure storing s.t. we can answer in O(1) time :
Does ? for any given .
Hashing
Hash
tab

CS648 : Randomized Algorithms
Semester I, 2013-14, CSE, IIT Kanpur
Why does Quick Sort behave as expected almost always ?
It is well known that the average running time of quick sort is O(n log n) time. We analysed randomized
quick sort earlier and showed

Randomized Algorithms
CS648
Lecture 1
1
Overview of the lecture
What is a randomized algorithm ?
Motivation
The structure of the course
2
What is a randomized algorithm ?
3
Deterministic Algorithm
Output
Input
Algorithm
The output as well as the runnin